Polygon Parallel Sides
1. The problem asks for the number of pairs of parallel sides in each polygon.
2. From the given data:
- Polygon 34 has 2 pairs of parallel sides.
- Polygon 35 has 1 pair of parallel sides.
- Polygon 36 has 4 pairs of parallel sides.
- Polygon 37 has 0 pairs of parallel sides.
3. Next, petrol costs are given for garages A, B, and C, and Carol needs to fill 20 litres.
- Garage A: 137p per litre, so cost = $20 \times 137 = 2740$ pence = 27.40 pounds.
- Garage B: 139p per litre, so cost = $20 \times 139 = 2780$ pence = 27.80 pounds.
- Garage C: 138p per litre, so cost = $20 \times 138 = 2760$ pence = 27.60 pounds.
4. Carol has 27.50 pounds.
- Garage A cost: 27.40 pounds (affordable)
- Garage B cost: 27.80 pounds (not affordable)
- Garage C cost: 27.60 pounds (not affordable)
5. Carol should go to garage A to fill up her car.
6. The most expensive garage is B at 27.80 pounds.
- Additional money needed = $27.80 - 27.50 = 0.30$ pounds.
7. Watch gains 2 minutes every 24 hours.
- From 10 a.m. to 10 p.m. same day is 12 hours, so watch gains $\frac{2}{24} \times 12 = 1$ minute.
- At 10 p.m. same night, watch shows 10:01 p.m.
8. From 10 a.m. Monday to 10 a.m. Tuesday (24 hours), watch gains 2 minutes.
- So at 10 a.m. Tuesday, watch shows 10:02 a.m.
9. From 10 a.m. Monday to 10 a.m. Wednesday (48 hours), watch gains $2 \times 2 = 4$ minutes.
- So at 10 a.m. Wednesday, watch shows 10:04 a.m.
10. From 10 a.m. Monday to 10 a.m. next Monday (7 days = 168 hours), watch gains $\frac{2}{24} \times 168 = 14$ minutes.
- So at 10 a.m. next Monday, watch shows 10:14 a.m.
11. Jasmina and Sharon shared 24 book tokens.
- Jasmina had 2 more than Sharon.
- Let Sharon have $x$ tokens, then Jasmina has $x + 2$.
- Total: $x + (x + 2) = 24 \Rightarrow 2x + 2 = 24 \Rightarrow 2x = 22 \Rightarrow x = 11$.
- Sharon has 11 tokens, Jasmina has 13 tokens.
12. Minutes between noon and 13:29:
- 1 hour 29 minutes = $60 + 29 = 89$ minutes.
13. Weeks in 266 days:
- $\frac{266}{7} = 38$ weeks (ignoring remainder).
Final answers:
- Polygon pairs: 34=2, 35=1, 36=4, 37=0
- Garage choice: A
- Extra money needed: 0.30
- Watch times: 10:01 p.m. Monday, 10:02 a.m. Tuesday, 10:04 a.m. Wednesday, 10:14 a.m. next Monday
- Tokens: Jasmina 13, Sharon 11
- Minutes: 89
- Weeks: 38